If (x,3),(6,3),(8,2) and (9,4) are the vertices of a parallellogram taken in order ,then find the value of x and y.​

1 thought on “If (x,3),(6,3),(8,2) and (9,4) are the vertices of a parallellogram taken in order ,then find the value of x and y.​”

1. Answer:

   Let A be the (x, 3), B be the (6,3), C be the (8,2) and D be the (9,4)

   A = (x1,y1) = (x, 3)

   B = (x2,y2) = (6,3)

   C = (x3,y3) = (8,2)

   D = (x4,y4) = (9,4)

   It is given that ABCD is a parallelogram.

   Diagonals of the parallelogram bisect each other.

   Mid-point of AC = Mid-point of BD

   Mid-point of AC = x1 + x3/2 , y1 + y3/2

   = x + 8/2 , 3 + 2/2

   = x + 8/2 , 5/2

   Mid-point of BD = x2 + x4/2 , y2 + y4/2

   = 6 + 9 /2 , 3 + 4/2

   = 15/2 , 7/2

   x + 8/2 = 15/2

   x + 8 = 15

   x = 15- 8

   x = 7

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